51 Mathematik
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Varying thermal stresses influence significantly the time to failure of electric components as used, for instance, in automotive devices. For applications as autonomous driving a high reliability has to be guaranteed.
In this article we discuss how to combine probability distributions for failure. Discrete and continuous changes of the probability distribution in time are both considered. It turns out that the temporal order of the distributions, corresponding to the succession of stresses in applications, is essential.
The latter observation restricts the general applicability of the widely used temperature collectives where only the total time of a temperature stress is considered neglecting the order of the stresses.
An application of our results are thermal overstress tests on electric components. We may explain yet not well understood measurements for automotive electric cables.
Knowing about the presence and number of people in a room can be of interest for precise control of heating, ventilation and air conditioning. To determine the number and presence of occupants cost-effectively, it is of interest to use already existing air condition sensors (temperature, humidity, CO2) of the building automation system. Different approaches and methods for determining presence have attracted attention in recent years. We propose an occupancy detection method based on a method of supervised machine learning. In an experiment, measurement data were recorded in a research apartment with controllable boundary conditions. The presence of people was simulated by artificial injection of water vapour, CO2 and heat dissipation. The variation of the number of artificial users, the duration of presence and the supply air volume flow of the ventilation resulted in a total of 720 combinations. By using artificial users, the boundary conditions were accurately defined, and different presence situations could be measured time-effectively. The data is evaluated with a method of supervised machine learning called random forest. The statistical model can determine precisely the number of people in over 93% of the cases in a disjoint test sample. The experiments took part in the Rosenheim Technical University of Applied Sciences laboratory.
The energy efficiency of the building HVAC systems can be improved when faults in the running system are known. To this day, there are no cost-efficient, automatic methods that detect faults of the building HVAC systems to a satisfactory degree. This study induces a new method for fault detection that can replace a graphical, user-subjective evaluation of a building data measured on site with an automatic, data-based approach. This method can be a step towards cost-effective monitoring. For this research, the data from a detailed simulation of a residential case study house was used to compare a faultless operation of a building with a faulty operation. We argue that one can detect faults by analysing the properties of residuals of the prediction to the actual data. A machine learning model and an ARX model predict the building operation, and the method employs various statistical tests such as the Sign Test, the Turning Point Test, the Box-Pierce Test and the Bartels-Rank Test. The results show that the amount of data, the type and density of system faults significantly affect the accuracy of the prediction of faults. It became apparent that the challenge is to find a decision rule for the best combination of statistical tests on residuals to predict a fault.
Faults in Heating, Ventilation and Air Conditioning (HVAC) systems affect the energy efficiency of buildings. To date, there rarely exist methods to detect and diagnose faults during the operation of buildings that are both cost-effective and sufficient accurate. This study presents a method that uses artificial intelligence to automate the detection of faults in HVAC systems. The automated fault detection is based on a residual analysis of the predicted total heating power and the actual total heating power using an algorithm that aims to find an optimal decision rule for the determination of faults. The data for this study was provided by a detailed simulation of a residential case study house. A machine learning model and an ARX model predict the building operation. The model for fault detection is trained on a fault-free data set and then tested with a faulty operation. The algorithm for an optimal decision rule uses various statistical tests of residual properties such as the Sign Test, the Turning Point Test, the Box-Pierce Test and the Bartels-Rank Test. The results show that it is possible to predict faults for both known faults and unknown faults. The challenge is to find the optimal algorithm to determine the best decision rules. In the outlook of this study, further methods are presented that aim to solve this challenge.
Im Gemeinde- und Landkreiswahlgesetz haben Listenverbindungen eine lange Tradition. Sie sollen bei der Verrechnung von Stimmen in Sitze Verzerrungen dämpfen, die mit dem D’Hondt-Verfahren auftreten können. Da aber die Sitzzuteilung seit 2010 mit dem unverzerrten Hare/Niemeyer-Verfahren vorgenommen wird, haben Listenverbindungen ihre Berechtigung verloren. Wir demonstrieren die Problematik anhand der Kommunalwahlen 2014. In mehreren Kommunen passierte es, dass von zwei Listen diejenige mit mehr Stimmen weniger Sitze erhielt, was mit der Erfolgswertgleichheit der Wählerstimmen unvereinbar ist. Auch kam es vor, dass eine Liste den Einzug in den Gemeinderat nur deshalb verfehlte, weil sie einer Listenverbindung angehörte.
Analysis of M/G/1-queues with Setup Times and Vacations under Six Different Service Disciplines
(2001)
Single server M/G/1-queues with an infinite buffer are studied; these permit inclusion of server vacations and setup times. A service discipline determines the numbers of customers served in one cycle, that is, the time span between two vacation endings. Six service disciplines are investigated: the gated, limited, binomial, exhaustive, decrementing, and Bernoulli service disciplines. The performance of the system depends on three essential measures: the customer waiting time, the queue length, and the cycle duration. For each of the six service disciplines the distribution as well as the first and second moment of these three performance measures are computed. The results permit a detailed discussion of how the expected value of the performance measures depends on the arrival rate, the customer service time, the vacation time, and the setup time. Moreover, the six service disciplines are compared with respect to the first moments of the performance measures.
In dieser Arbeit werden M/G/1-Warteschlangen mit unendlich großem Warteraum und einem Server, der Bedienpausen und Bereitstellungszeiten benötigt, für die absperrende, begrenzende, binomiale, entleerende, vermindernde und bernoullische Bediendisziplin untersucht. Dabei bestimmt die Bediendisziplin, wie viele Kunden der Server in einem Zyklus, das ist die Zeit zwischen zwei Pausenenden, bedient.
Wichtige Kenngrößen eines solchen Modells sind die Wartezeit eines Kunden, die Warteschlangenlänge zu einem beliebigen Zeitpunkt und die Zyklusdauer. Für jede der sechs Bediendisziplinen werden die Verteilung und die ersten beiden Momente dieser Kenngrößen berechnet.
Die Ergebnisse werden benutzt, um die Abhängigkeit der ersten Momente der Kenngrößen von der Ankunftsrate, der Kundenbediendauer, der Pausenlänge und der Dauer der Bereitstellungszeit zu untersuchen. Ferner werden die sechs Bediendisziplinen bezüglich der Erwartungswerte der Kenngrößen miteinander verglichen.